Spectral theory of hypergraphs

Spectral hypergraph theory studies the qualitative properties of a hypergraph that can be inferred from the eigenvalues and the eigenvectors of either square matrices or tensors associated with it. It generalizes the spectral theory of graphs, which has a long history and is widely used in applications. In this talk we will recall some key results in spectral graph theory before discussing spectral hypergraph theory, both via matrices and via tensors. We will also compare these two different techniques, and we will see some applications to dynamical systems and data analysis.